The main contribution of the paper is to propose OTFS based on the discrete Zak transform (DZT), which is motivated by the digital implementation of OFDM (see [1]}, [2]}, or [3]}). Unlike the work presented in [4]}, we do not create an OTFS waveform by introducing time and bandwidth limitations of the continuous Zak transform. Instead, we use the DZT, which can be obtained by discretizing the Zak domain [5]}. Second, based on the DZT, we derive the input-output relation of OTFS for TF dispersive channels. More specifically, by utilizing DZT signal transform properties, we show that the effect of TF dispersive channels corresponds to convolutions in the delay and Doppler domain. This approach not only simplifies the input-output relation but also furthers the understanding of OTFS.
